What is the tangent of f(x)=(x^2)/(x+5),\at x=3 ?

The tangent of f(x)=(x^2)/(x+5),\at x=3 is y= 39/64 x-45/64

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tangent of f(x)=(x^2)/(x+5),\at x=3

tangent of

f (x) = \frac{x ^{2}}{x + 5}, at x = 3

y = \frac{39}{64} x - \frac{45}{64}

Solution steps

Find the tangent point:

(3, \frac{9}{8})

Find the slope of

f (x) = \frac{x ^{2}}{x + 5} : \frac{df ( x )}{d x} = \frac{x ^{2} + 10 x}{( x + 5 ) ^{2}}

Compute the slope of

f (x) = \frac{x ^{2}}{x + 5}

x = 3 : m = \frac{39}{64}

Find the line with slope m=

\frac{39}{64}

and passing through

(3, \frac{9}{8}) : y = \frac{39}{64} x - \frac{45}{64}

y = \frac{39}{64} x - \frac{45}{64}

a q^{2}

2 x - x^{2}, 2 x - 4

\frac{d}{d x} (sin (x) cot (x))

x \to 0 + lim (- \frac{2 + ln ( x )}{x})

\int_{0}^{2} π (8 - x^{3})^{2} d x

What is the tangent of f(x)=(x^2)/(x+5),\at x=3 ?
The tangent of f(x)=(x^2)/(x+5),\at x=3 is y= 39/64 x-45/64